Measure and prep all of your ingredients and keep them near the stove (measure the spices into a bowl, open the coconut milk, chop the veggies, etc). In a Dutch oven or similar large, deep skillet, heat the oil over medium heat. Once it is hot and shimmering, add curry paste, onion, garlic, ginger, cumin, coriander, and cinnamon. Cook, stirring constantly, until the paste darkens and the spices smell ultra fragrant, 2 to 3 minutes.
Stir in the full-fat and light coconut milk, potatoes, carrots, fish sauce, peanut butter, and salt. If needed, use a whisk to blend everything together until smooth.
Bring to simmer. Cook until potatoes and carrots are barely tender, stirring periodically, about 12 minutes.
Stir in the chicken. Continue simmering, stirring periodically, until chicken is cooked through, about 10 to 12 minutes more.
Remove from the heat. Zest the lime directly into the pot, then squeeze in the juice. Serve over cooked rice with a generous sprinkle of chopped peanuts and cilantro.
Notes
TO STORE: Refrigerate curry in an airtight storage container for up to 4 days.
TO REHEAT: Rewarm leftovers in a pot on the stovetop over medium-low heat or in the microwave.
TO FREEZE: Freeze curry in an airtight, freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.